SOLUTION: The numerator of a certain fraction is 3 less than its denominator. If 6 is added to the numerator and 5 to the denominator, the value of the fraction is doubled. Find the f

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Question 1018499: The numerator of a certain fraction is 3 less than its denominator. If 6 is added to
the numerator and 5 to the denominator, the value of the fraction is doubled.
Find the fraction.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
n%2Fd, the fraction.

system%28n=-3%2Bd%2C%28n%2B6%29%2F%28d%2B5%29=2%28n%2Fd%29%29

%28n%2B6%29%2F%28d%2B5%29=2n%2Fd
d%28n%2B6%29=2n%28d%2B5%29
substitute.
d%28d-3%2B6%29=2%28d-3%29%28d%2B5%29
removed%29
removed
removed
0=d%5E2%2B3d-30,
removed

-removed-

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I will recheck.

Step should be %28d%2B3%29%2F%28d%2B5%29=2%28d-3%29%2Fd
and then
%28d%2B5%29%282d-6%29=d%28d%2B3%29
and skipping past a few steps,...
d%5E2%2Bd-30=0
which will give EITHER d=-5 OR d=6.
You can work toward finding n from there.

-
I later checked these results thoroughly. The d=-5 part will not work; but the d=6 part works perfectly, indicating highlight%28n%2Fd=1%2F2%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The numerator of a certain fraction is 3 less than its denominator. If 6 is added to
the numerator and 5 to the denominator, the value of the fraction is doubled.
Find the fraction.